Abstract
The critical behavior of spin systems with quenched disorder is studied by renormalization-group methods. For the randomly dilute -vector model, the limit is used to construct a translationally invariant effective Hamiltonian which describes the original disordered system. This Hamiltonian is analyzed in the expansion to order . Sharp second-order phase transitions with exponents which do not depend continuously on impurity concentration are predicted. For the isotropic -component fixed point, which characterizes the critical behavior of the pure system, is stable. For , a new random fixed point becomes stable. The exponents corresponding to this fixed point are , for , and , for . More general random systems are qualitatively discussed from the effective-Hamiltonian viewpoint.
- Received 16 September 1975
DOI:https://doi.org/10.1103/PhysRevB.13.1329
©1976 American Physical Society